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Fractal Characteristics of Newton's Method on Polynomials

Abstract:

In this report, we present a simple geometric generation principle for the fractal that is obtained when applying Newton's method to find the roots of a general complex polynomial with real coefficients. For the case of symmetric polynomials $z^{\nu}-1$ , the generation mechanism is derived from first principles. We discuss the case of a general cubic and are able to give a description of the arising fractal structure depending on the coefficients of the cubic. Special cases are analysed and ...

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Publisher:
Unspecified
Publication date:
1996-11-01
UUID:
uuid:b5bc3292-b508-494d-ac4c-17db80572423
Local pid:
oai:eprints.maths.ox.ac.uk:1323
Deposit date:
2011-06-12

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